in a rotating disc,how can linear velocity vary linearly with the distance from the center?

Question

assuming that angular velocity is constant & axis of rotation is thro' the center of the disc,how does the circular disc distribute the tangential velocity linearly (i.e. ang vel * radius) along the radius.
alternately what does one mean by velocity increasing radially and how is this achieved by the material of the disc?

Answer 1

V = omega * R

R - radius
omega - angular velocity
V- linear levocity.

If you imagine a rotating wheel and you put a little rat on the rim. Now rotate the wheel. Rat will be travelling pretty fast, right? (You're observing linear velocity now.) Now move the rat close to the axis of rotation. Now your rat is hardly travelling at all. But his old seat is travelling pretty fast. This is what one mean by velocity increasing radially.

Answer 2

If you use the formula that at any distance 'r' from the centre the circumference is '2*pi*r'. i.e the distance travailed is proportional to the radius. Hence when the disc rotates, to keep all the materials intact, the linear velocity at the circle of radius r, should be the same. Moreover this velocity is equal to 'omega' the angular velocity times the radius. Hence the linear velocity is proportional to radius 'r' will only keep the material of the disc in place.

Answer 3

Is yahoo doing your first year homework?

The velocity at any place on the disc is a linear function of the distance from the axis of rotation assuming a constant angular rate of rotation omega.

Answer 4

velocity = radius * angular velocity is a linear relationship.

velocity increasing radially means that as the radius increases the velocity increases. This is achieved by the ability of the disc not to disintegrate, or cohesiveness (tensile strength)

Answer 5

By tension and compression of its material from center outward.